This note addresses the adaptive consensus problem of first-order and second-order linearly parameterized multi-agent systems with unknown identical control directions. First, we propose a new Nussbaum-type function based on which a key lemma is established. The lemma plays an important role in analyzing the consensus of the closed-loop multi-agent systems. Second, the Nussbaum-type function is used to design adaptive control laws for first-order and second-order linearly parameterized multi-agent systems so that each agent seeks for the unknown control direction adaptively and cooperatively. Then, under the assumption that the interconnection topology is undirected and connected, it is proved that the first-order and second-order multi-agent systems can achieve consensus by choosing proper design parameters. Two simulation examples are given to illustrate the effectiveness of the proposed control laws.